Over R, the 2×2 matrix is diag(0,13). Give its distinct real eigenvalues as an increasing set with each value once.
G001 — Over R, the 2×2 matrix is diag(0,13). Give its distinct real eigenvalues as an increasing set with each value once.
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Check THIS source interface:distance uses ONLY its complete coordinate frame;other families use a domain.Discrete operations use local hyphens,legacy banks underscores.Retain family-specific ordered output types and original bilingual data/status.
For diag(a,d),the characteristic factors are(a−λ)(d−λ),so the roots are a,d.Return the DISTINCT numerically sorted set,deduplicating equal roots.Zero is not an empty set;this is not a multiplicity list.
S002 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,types and premises;the conclusion need not uniquely recover its premises.This source-bound candidate is not independent review or formal proof.
S001 · premise_and_result_audit — Reverse-check the ORIGINAL inputs,types and premises;the conclusion need not uniquely recover its premises.This source-bound candidate is not independent review or formal proof.
Result
{0, 13}
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.